0.32x+x^2=0.84

Solution for 0.32x+x^2=0.84 equation:

0.32x+x^2=0.84

We move all terms to the left:

0.32x+x^2-(0.84)=0

We add all the numbers together, and all the variables

x^2+0.32x-0.84=0

a = 1; b = 0.32; c = -0.84;
Δ = b2-4ac
Δ = 0.322-4·1·(-0.84)
Δ = 3.4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.32)-\sqrt{3.4624}}{2*1}=\frac{-0.32-\sqrt{3.4624}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.32)+\sqrt{3.4624}}{2*1}=\frac{-0.32+\sqrt{3.4624}}{2}
$